Sin^2 (15Pi/4-2x) - cos^2 (17Pi/4-2x) = упростить. с решением

Sin² (15π/4 - 2x) - cos² (17π4 - 2x) = sin² (16π/4 - π/4 - 2x) - cos² (16π/4+π/4 - 2x) =

=sin² (4π - (π/4+2x)) - cos² (4π+π/4-2x) = sin² (π/4+2x) - cos² (π/4-2x) =

= (sinπ/4·cos2x+cosπ/4·sin2x) ² - (cosπ/4·cos2x+sinπ/4·sin2x) ²=

= (√2/2·cos2x+√2/2·sin2x) ² - (√2/2·cos2x+√2/2·sin2x) ²=

=[√2/2· (cos2x+sin2x) ]²-[√2/2· (cos2x+sin2x) ]²=0;